 Kun tutkittavuutta on tullut tullut data-analysisen, se on tullut tullut tullut tullut varavallisissa. Tämä on tullut siksi. Mutta ei ole mitään, joka tarvitaan tullut tullut tullut tullut tullut varavallisissa. Mennään koko, mitä on tullut, kun tullut tullut tullut varavallisissa. Joten tullut tullut tullut tullut tullut, on X1, X2 ja X3, jotka tullut tullut varavallisissa, on käytännössä eri perustastuksia tarvi. Täällä on kolme esitellä, X11 on ensimmäinen esitellä, tämä esite on ensimmäinen esitellä, X12 on tullut tullut saman esitellään. Tällä erityksen tullut tullut, X13 on tullut saman esitellä, tämä mennä tällä eri tullut. Nykyään, mitä on pitänyt mitis vastauksia langitunnelilä-analysisille. Sitten tihe intendellä rapaajasta. Tämä on två eritylipuolio. Se, että noussimme sen, when we do longitudinal modeling of latent variables. The first thing is that we need to understand what these error terms are about. So error terms typically, they capture unreliability, but they also capture item uniqueness. So there might be something in X11 that is or the first indicator that is persistent over time that is different from the second indicator. So quite often we want to say that the first indicator's uniqueness correlates over time. So we have these correlations over time of these measurement errors. So that is the first special thing that you need to consider when you do longitudinal analysis of latent variables. Another thing is measurement environments. Measurement environments briefly means that your measurement model works the same way or the measurement process works the same way between X1 and X2 and X2 and X3. This is important because it is possible that the skeptic to our argument says that there is actually no correlation between X1 and X2, rather this is a measurement defect. Or if we are looking at levels, one could say that X2 has a higher mean than X1, not because there are attributes of interest as evolved over time, but simply because our measurement process works differently between the first and second time point. We need to consider measurement invariance, which I explain in more detail in another video, to address this concern. Let's take a look at two examples of what a longitudinal latent variable model would look like. So this is a crosslock model without random intercepts. We can see that we have positive effect, negative effect. There is the correlation between error terms in the same time. We have the autoregressive terms here, the paths here and the crosslock paths here. And we can see that the errors are all to be correlated, so that the first indicator correlates always with the first indicator at different time points. So all the first indicator observations are allowed to be freely correlated, all the second indicator observations are allowed to be freely correlated, and all the third indicator observations are allowed to be freely correlated. So this is the correlation over time. The same thing can be seen also in this latent change model. So instead of having observed variables here, we have latent variables and we have means, which are typically of interest when we want to model change over time, and we have these correlated error terms that allow the uniqueness to persist over time.